The Rebels have made a habit of close defeats in their third season in the competition but held on for their third win of the year to hand the Stormers a third straight defeat and put their hopes of a playoff berth in jeopardy.
The key moment of the match came with six minutes remaining when replacement scrumhalf Nick Phipps hacked a loose ball through but was held back by Stormers hooker Martin Bezuidenhout as he scurried after it.
The television review official felt the Wallaby would have scored a try had he not been impeded and the Rebels went from trailing by a point to leading by six with the Stormers down to 14 men as Bezuidenhout languished in the sin bin.
Fullback Jason Woodward then kicked his third penalty with a minute remaining to seal the victory and delight the Melbourne crowd.
"That's fantastic, credit to the boys we hung in there and we played a great game of footie tonight," said Higginbotham, who was without two other Wallabies in the injured James O'Connor and the suspended Kurtley Beale.
"We stood up to them, it was great. It's a great positive for the boys and we'll take that into next week."
Back row forward Higginbotham had scored his sixth try of the season after just 12 minutes to confirm his fine form ahead of his almost certain selection for the series against the British and Irish Lions.
A break from the number eight also established the platform from which smart work from Phipps allowed lock Hugh Pyle to score and put the Rebels back in front 20-14 in the 54th minute.
The Stormers had led 14-13 at halftime, though, courtesy of tries from scrumhalf Louis Schreuder and winger Bryan Habana - his 54th in Super Rugby - and they retook the lead through a converted try from lock Andries Bekker on the hour mark.
The Rebels withstood a 10-minute barrage of pressure after going behind and the Stormers will rue not letting fullback Joe Pietersen have a crack at some very kickable penalties, particularly as he was error-free with the boot for the second successive week.
"That was embarrassing," skipper Juan de Villiers said. "I think that's just not good enough and hard decisions will have to be made now."
- Sports & Recreation
- Martin Bezuidenhout